2,061 research outputs found
Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables
We propose an approach for learning the causal structure in stochastic
dynamical systems with a -step functional dependency in the presence of
latent variables. We propose an information-theoretic approach that allows us
to recover the causal relations among the observed variables as long as the
latent variables evolve without exogenous noise. We further propose an
efficient learning method based on linear regression for the special sub-case
when the dynamics are restricted to be linear. We validate the performance of
our approach via numerical simulations
Supervised estimation of Granger-based causality between time series
Brain effective connectivity aims to detect causal interactions between distinct brain units and it is typically studied through the analysis of direct measurements of the neural activity, e.g., magneto/electroencephalography (M/EEG) signals. The literature on methods for causal inference is vast. It includes model-based methods in which a generative model of the data is assumed and model-free methods that directly infer causality from the probability distribution of the underlying stochastic process. Here, we firstly focus on the model-based methods developed from the Granger criterion of causality, which assumes the autoregressive model of the data. Secondly, we introduce a new perspective, that looks at the problem in a way that is typical of the machine learning literature. Then, we formulate the problem of causality detection as a supervised learning task, by proposing a classification-based approach. A classifier is trained to identify causal interactions between time series for the chosen model and by means of a proposed feature space. In this paper, we are interested in comparing this classification-based approach with the standard Geweke measure of causality in the time domain, through simulation study. Thus, we customized our approach to the case of a MAR model and designed a feature space which contains causality measures based on the idea of precedence and predictability in time. Two variations of the supervised method are proposed and compared to a standard Granger causal analysis method. The results of the simulations show that the supervised method outperforms the standard approach, in particular it is more robust to noise. As evidence of the efficacy of the proposed method, we report the details of our submission to the causality detection competition of Biomag2014, where the proposed method reached the 2nd place. Moreover, as empirical application, we applied the supervised approach on a dataset of neural recordings of rats obtaining an important reduction in the false positive rate
Discovering Graphical Granger Causality Using the Truncating Lasso Penalty
Components of biological systems interact with each other in order to carry
out vital cell functions. Such information can be used to improve estimation
and inference, and to obtain better insights into the underlying cellular
mechanisms. Discovering regulatory interactions among genes is therefore an
important problem in systems biology. Whole-genome expression data over time
provides an opportunity to determine how the expression levels of genes are
affected by changes in transcription levels of other genes, and can therefore
be used to discover regulatory interactions among genes.
In this paper, we propose a novel penalization method, called truncating
lasso, for estimation of causal relationships from time-course gene expression
data. The proposed penalty can correctly determine the order of the underlying
time series, and improves the performance of the lasso-type estimators.
Moreover, the resulting estimate provides information on the time lag between
activation of transcription factors and their effects on regulated genes. We
provide an efficient algorithm for estimation of model parameters, and show
that the proposed method can consistently discover causal relationships in the
large , small setting. The performance of the proposed model is
evaluated favorably in simulated, as well as real, data examples. The proposed
truncating lasso method is implemented in the R-package grangerTlasso and is
available at http://www.stat.lsa.umich.edu/~shojaie.Comment: 12 pages, 4 figures, 1 tabl
Graphical modelling of multivariate time series
We introduce graphical time series models for the analysis of dynamic
relationships among variables in multivariate time series. The modelling
approach is based on the notion of strong Granger causality and can be applied
to time series with non-linear dependencies. The models are derived from
ordinary time series models by imposing constraints that are encoded by mixed
graphs. In these graphs each component series is represented by a single vertex
and directed edges indicate possible Granger-causal relationships between
variables while undirected edges are used to map the contemporaneous dependence
structure. We introduce various notions of Granger-causal Markov properties and
discuss the relationships among them and to other Markov properties that can be
applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related
Field
Detecting and quantifying causal associations in large nonlinear time series datasets
Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields
Sparse Learning for Variable Selection with Structures and Nonlinearities
In this thesis we discuss machine learning methods performing automated
variable selection for learning sparse predictive models. There are multiple
reasons for promoting sparsity in the predictive models. By relying on a
limited set of input variables the models naturally counteract the overfitting
problem ubiquitous in learning from finite sets of training points. Sparse
models are cheaper to use for predictions, they usually require lower
computational resources and by relying on smaller sets of inputs can possibly
reduce costs for data collection and storage. Sparse models can also contribute
to better understanding of the investigated phenomenons as they are easier to
interpret than full models.Comment: PhD thesi
The connected brain: Causality, models and intrinsic dynamics
Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain. Over the past two decades, functional neuroimaging has emerged as the predominant technique in systems neuroscience. This is foreshadowed by an ever increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. In this article, we summarize pedagogically the (deep) history of brain mapping. We will highlight the theoretical advances made in the (dynamic) causal modelling of brain function - that may have escaped the wider audience of this article - and provide a brief overview of recent developments and interesting clinical applications. We hope that this article will engage the signal processing community by showcasing the inherently multidisciplinary nature of this important topic and the intriguing questions that are being addressed
A time series causal model
Cause-effect relations are central in economic analysis. Uncovering empirical cause-effect relations is one of the main research activities of empirical economics. In this paper we develop a time series casual model to explore casual relations among economic time series. The time series causal model is grounded on the theory of inferred causation that is a probabilistic and graph-theoretic approach to causality featured with automated learning algorithms. Applying our model we are able to infer cause-effect relations that are implied by the observed time series data. The empirically inferred causal relations can then be used to test economic theoretical hypotheses, to provide evidence for formulation of theoretical hypotheses, and to carry out policy analysis. Time series causal models are closely related to the popular vector autoregressive (VAR) models in time series analysis. They can be viewed as restricted structural VAR models identified by the inferred causal relations.Inferred Causation, Automated Learning, VAR, Granger Causality, Wage-Price Spiral
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